Semiconductor nano-wire antenna solar cells and detectors

ABSTRACT

Patterning planar photo-absorbing materials into arrays of nanowires is demonstrated as a method for increasing the total photon absorption in a given thickness of absorbing material. Such a method can provide faster, cheaper, and more efficient photo-detectors and solar cells. A thin nanowire can absorb many more photons than expected from the size of the nanowire. The reason for this effect is that such nanowires support cylindrical particle resonances which can collect photons from an area larger than the physical cross-section of the wire. These resonances are sometimes referred to as Mie resonances or Leaky Mode Resonances (LMRs). The nanowires can have various cross section shapes, such as square, circle, rectangle, triangle, etc.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. provisional patentapplication No. 61/340,125, filed on Mar. 12, 2010, entitled“Semiconductor Nano-wire Antenna Solar Cells and Detectors”, and herebyincorporated by reference in its entirety.

GOVERNMENT SPONSORSHIP

This invention was made with Government support under contract numberFA9550-06-1-0470 awarded by the Air Force Aerospace Research OSR. TheGovernment has certain rights in this invention.

FIELD OF THE INVENTION

This invention relates to optical absorption devices for detector andenergy applications.

BACKGROUND

Photo-absorbing materials form the basis for optoelectronicsapplications, such as photo-detectors or solar cells, where photons areabsorbed and converted into electrical signals. Typically, thephoto-absorbing material is laid down in a planar geometry. Manymaterials do not absorb photons efficiently and thick layers (100 s ofnanometers to 100 s of microns) are required to absorb the majority ofthe incident photons.

The large-scale implementation of photovoltaic (PV) technology aroundthe world would greatly benefit from further cost reductions in themanufacturing of solar modules. Moreover, it is important to identifynew ways to reduce the amount of semiconductor material used in PVcells, particularly for those cells employing non-earth-abundantelements like indium (CuInGaSe or CIGS cells) or tellurium (CdTe cells).Whereas thin film PV cells offer a viable pathway to reduce fabricationcosts and material usage, their energy conversion efficiencies can stillbe improved significantly by enabling them to harness a larger fractionof the incident solar photons. As a result, researchers are diligentlysearching for new approaches to dramatically boost the amount of lightabsorption per unit volume of semiconductor.

In addition to conventional anti-reflection coatings, reflectivesubstrates, and textured surfaces, more advanced light trappingtechniques based on resonant cavities, plasmonics, and photonic crystalshave recently gained significant interest. The best imaginable photonmanagement (PM) technology would effectively trap and/or concentratelight in a broadband, angle-independent, and polarization-independentfashion. Resonant PM structures have demonstrated significant promise,but their performance is typically limited by a fundamental trade-offbetween the attainable absorption enhancement and their operationalbandwidth. Moreover, resonant structures tend to exhibit a stronglyangle-dependent optical response and the resulting solar cells requirebulky solar tracking systems to follow the sun's movement in order tomaximize their daily energy output. The fabrication of more advanced PMstructures that could mitigate some of these issues is typicallyexpensive and the increased cost offsets the potential performancegains.

Nano-wires (or nano-rods) have been employed in connection with solarcells in the art. Typically, the nano-wires are disposed vertically on asubstrate (i.e., a “bed of nails” geometry). Representative examplesinclude US 2006/0207647, US 2007/0111368 and US 2008/0047604. Lateralillumination of nano-wires has also been considered, e.g., as in US2009/0188552.

SUMMARY

In this work, patterning planar photo-absorbing materials into arrays ofrods is demonstrated as a method for increasing the total photonabsorption in a given thickness of absorbing material. Such a method canprovide faster, cheaper, and more efficient photo-detectors and solarcells. In this description, the terms nano-rod, nano-beam, and nano-wire(and also “wire”, “beam”, and “rod”) are regarded as synonyms of eachother.

This work has shown that a thin nanowire can absorb many more photonsthan expected from the size of the nanowire. The reason for this effectis that such nanowires support cylindrical particle resonances which cancollect photons from an area larger than the physical cross-section ofthe wire. These resonances are sometimes referred to as Mie resonancesor Leaky Mode Resonances (LMRs). A schematic of such a device is shownin FIGS. 1 a-c. Here nano-wire 102 is separated from a substrate 110with an insulator 108. Terminals 104 and 106 provide electrical contactto nano-wire 102. FIG. 1 c is a top view, and FIGS. 1 a-b are twoorthogonal side views. The measured absorption efficiencies agree wellwith analytical models based on cylindrical particles (FIG. 1 d) andsuggest that such rods could be excellent building blocks forphoto-absorbing applications such as photo-detectors and solar cells. Animportant feature of the geometry of FIGS. 1 a-c is that the nano-wireis disposed laterally on the substrate.

For practical applications, it is desirable to scale up thesingle-particle concept to an array which covers a large area, caneasily be fabricated, and takes advantage of the small radius of therods. Via known etch step and/or thin-film deposition techniques, aplanar film 202 (FIG. 2 a) can be processed to provide an array 204 ofrectangular (w≠t) or square (w=t) rods (FIG. 2 b), which can cover alarge area. Alternatively, rather than covering the entire lightcollection area with active material, an array of polymer micro-lenses208 can focus light 210 down onto a sparse array 206 of photo-absorbingrods (FIG. 2 c). A single square rod supports quasi-cylindrical modeswhich are very similar to that of a rod with circular cross-section andsimilar enhancements in the absorption can be observed for this geometry(FIG. 2 d). Here, the curves labeled C-TM and S-TM are for transversemagnetic (TM) polarization and circular and square rod cross sections,respectively. Similarly, the curves labeled C-TE and S-TE are fortransverse electric (TE) polarization and circular and square rod crosssections, respectively. The photonic modes in the original filmcorrespond to light interacting with planar structures. Aftermodification, the relevant photonic modes correspond to lightinteracting with quasi-cylindrical structures. Any solar-cell orphoto-detector device layout can be readily modified to work in this newgeometry. We show a simple example in FIGS. 3 a-b. Here active material304 is patterned into nano-rods which are vertically sandwiched betweenelectrodes 302 and 306. FIG. 3 b is a top view, and FIG. 3 a is a sideview along line 310 of FIG. 3 b. A significant feature of the example ofFIGS. 3 a-b is that current flows across the width (−10 s to 100 s ofnms) of the nano-rods, in contrast to the situation in FIGS. 1 a-c,where current flows along the length (˜1.5micron) of the nano-rod. Theimplications of this are further described below. The array of FIGS. 3a-b has nano-wires disposed laterally on the substrate.

Our simulations show that the rod array films can have more photonabsorption than an unstructured film of the same thickness. Theimplication of this technique is that we can use thinner photo-absorbingregions to accomplish the same amount of photon absorption. This canresult in a number of important technical advantages. First, high-speedphotodetectors can be made to operate faster, as less time is requiredfor the generated carriers to transit the device (because they musttravel a smaller distance). Second, solar cells and photodetectors canbe made more efficient as carriers are less likely to encounter trapsand defects as they traverse a shorter distance. This fact could beespecially useful for devices made of amorphous Silicon, Germanium, andother semiconductors, which typically have poor electrical transportcharacteristics. Third, the modified device uses less photo-absorbingmaterial and thus can potentially be made cheaper and in a shorter time.

Significant aspects of the present approach include:

-   a) The use of enhanced absorption effects in quasi-cylindrical    structures; and-   b) Further refinements, such as

i) Using rods of rectangular or square, rather than circular,cross-section;

ii) A simple technique for fabricating an array of rods withrectangular/square cross-section;

ii) Such rod arrays can cover a large area and have increased absorptionfor a given thickness film of photo-absorbing material; and

iii) The use of electrical transport along the small dimension of therods (height rather than length) for improved device performance.

A preferred embodiment focuses on the specific case of square rod andrectangular arrays, as we believe that geometry is the mosttechnologically relevant and easy to implement. However, a number ofmodifications are possible. We have performed simulations showing thatrods of differing cross-sections (circular, square, triangular) allsupport quasi-cylindrical rod modes, and we suspect that rods ofrectangular cross-section still exhibit such resonant modes. Although webelieve that top-down fabrication of square rods is the most readilyaccessible route for realizing a useful device, bottom-up growth ofarrays of nanowires is another potential method. Our investigations havefocused on the technologically important materials Si and Ge, which haverelatively large refractive indexes (n˜4). The proposed device may beparticularly useful for the amorphous forms of those materials. However,the quasi-cylindrical modes exist in materials of any refractive indexand thus the technique is broadly applicable, although the efficacylikely depends on the specific material in question. Finally, we notethat the technique can be applied to films of varying thicknesses byoptimizing the relevant array parameters. We believe that this approachcould be used in a large number of photo-detector and solar cellapplications to improve device performance. Generally, quasi-cylindricalresonance can be exploited to provide enhanced photo-absorption.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 a-c schematically show an exemplary embodiment of the invention.

FIG. 1 d is a plot of calculated and experimentally measured absorptionefficiency.

FIGS. 2 a-c schematically show another exemplary embodiment of theinvention.

FIG. 2 d is a plot of absorption spectra for circular and square rodcross sections.

FIGS. 3 a-b schematically show a further exemplary embodiment of theinvention.

FIG. 4 a is a plot of calculated and experimentally measured absorptionefficiency.

FIG. 4 b is a plot of photocurrent and photocurrent enhancement as afunction of nano-wire diameter.

FIG. 5 a is a plot of normalized photocurrent vs. incident angle forseveral different nano-wire diameters.

FIG. 5 b is a plot of measured and calculated absorption efficiency forseveral different incident angles.

FIG. 6 a is a plot of calculated photocurrent and photocurrentenhancement as a function of nano-wire diameter for several differentnano-wire materials.

FIG. 6 b is a plot of calculated photocurrent and photocurrentenhancement as a function of incident angle for several differentnano-wire materials.

FIG. 7 a is a plot of calculated photocurrent as a function of nano-wirediameter for several different nano-wire shapes.

FIG. 7 b is a plot of calculated absorption efficiency as a function ofwavelength for several different nano-wire shapes.

FIG. 8 a is a plot of calculated photocurrent and photocurrentenhancement as a function of nano-wire separation.

FIG. 8 b is a plot of normalized photocurrent vs. incident angle forseveral different nano-wire diameters.

FIG. 8 c is a plot of absorption efficiency vs. wavelength for severaldifferent nano-wire spacings and potentially non-periodic spacingbetween the nanowires.

FIGS. 9 a-b show further exemplary embodiments of the invention.

DETAILED DESCRIPTION

Photovoltaic (PV) cells can serve as a virtually unlimited clean sourceof energy by converting sunlight into electrical power. Their importanceis reflected in the tireless efforts that have been devoted to improvingthe electrical and structural properties of PV materials. More recently,photon management (PM) has emerged as a powerful additional means toboost energy conversion efficiencies. Here, we demonstrate an entirelynew PM strategy that capitalizes on strong broadband optical antennaeffects in one-dimensional semiconductor nanostructures to dramaticallyenhance absorption of sunlight. We show that by patterning thesemiconductor layer in a thin film PV cell into an array of nanowires(NWs), one can boost the short-circuit current by 25% while utilizingless than half of the semiconductor material (250% increase in currentper unit volume material). The NW's optical properties also naturallygive rise to an improved angular response. The approach is universal toany semiconductor and provides a new PV platform technology.

The use of optical antenna effects in 1-dimensional semiconductornanostructures enables significant enhancement in the absorption ofsunlight with little dependence on illumination angle. As sufficientlylarge diameter (about 100 nm or more) nanowires are known to alsoexhibit a polarization-independent response, they could serve as analmost ideal building block for PV systems. Building on this notion, weinvestigate a new type of high-performance PM strategy for solar cellsin which a thin semiconductor film is patterned into an array ofthoughtfully engineered one-dimensional nanostructures. The mostimportant benefits of this new PM strategy are the ease of fabricationand the broadband nature of the absorption enhancements which is derivedfrom the plurality of optical resonances in the wires that cover thesolar spectrum.

Arrays of semiconductor nanostructures with elongated shapes, such asNWs, nanorods, and nanopillars, have recently demonstrated significantpromise for photovoltaic applications; these structures can exhibit bothenhanced absorption and a reduced reflectivity as compared to planar,film-based devices. In this work, we demonstrate that semiconductor NWscan effectively serve as a set of broadband optical antennas forsunlight. As such, the NWs capture and absorb significantly more solarphotons than an equivalent volume of bulk material. We have demonstratedpowerful antenna effects in photocurrent measurements on Ge NWs atspecific wavelengths. When the illumination wavelength matched one ofthe allowed leaky mode resonances (LMRs), the high refractive index wirewas able to capture and trap the light by multiple internal reflectionsfrom its boundary. As a consequence, light absorption and the resultingphotocurrent could be enhanced at a desired wavelength by tuning the NWdiameter. Here, we illustrate how light absorption in NWs can beincreased over the tremendously broadband solar spectrum by takingadvantage of the plurality of spectrally-separated LMR resonancessupported by relative large (>100 nm) diameter structures. The nature ofthe antenna effects in NWs also naturally provides for a desirable weakangle- and polarization-dependence of the optical response.

In the following, we start with an experimental demonstration of opticalantenna effects in individual Si NWs, which form the basic buildingblocks of our proposed PV cells. We then continue with an optimizationof their absorption efficiencies by engineering the best possible matchbetween the absorption spectrum of the wires and the solar spectrum. Inthis exercise we not only show large absorption enhancements compared toplanar structures, but we also experimentally demonstrate the broadangular response. We continue by showing how this approach can beapplied to a great diversity of materials systems (including e.g.amorphous Si, CdTe, GaAs, CuInGeSe, and copper-zinc-tin-sulfur (CZTS)compositions) and wire geometries of different cross-sectional shape(e.g. circular, rectangular, hexagonal or triangular). We conclude byillustrating how the individual NW optimizations can be used to guidethe design of large-area devices consisting of a plurality of NWs.

In order to demonstrate the superior optical properties ofone-dimensional semiconductor nanostructures over films, we fabricated aset of metal-semiconductor-metal (MSM) photodetectors with individualcrystalline SiNWs (c-SiNWs). The c-SiNWs were grown by a gold-catalyzedchemical vapor deposition procedure and spectral absorption propertiesof the NWs were derived from photocurrent measurements. The measuredphotocurrent spectra for several c-SiNWs of different diameter are givenin FIG. 4 a.

FIGS. 4 a-b show leaky mode resonances (LMRs) and enhanced photocurrentdensity in silicon nanowires. FIG. 4 a shows measured (dashed) andcalculated (solid) spectral absorption efficiency Qabs of single Sinanowires with diameter of 100 nm, 200 nm, and 240 nm. The measuredresults were scaled by a constant factor over the entire spectrum tobest fit the calculations. FIG. 4 b (upper part) shows calculatedshort-circuit photocurrent density JSC for silicon nanowires (dottedline) and for bulk silicon (dashed line) of comparable thickness. Thesolid line indicates the photocurrent enhancement of the nanowire perunit volume of material; the expression used to calculate theenhancement is (JSC, NW/VNW−JSC, Bulk/VBulk)/(JSC, Bulk/VBulk). FIG. 4 b(lower part) Two-dimensional plot of the calculated absorptionefficiency Qabs of a crystalline silicon nanowire as functions of thewavelength and diameter. The distinct streaks of high intensity indicatethe presence of the various leaky mode resonances, with the first threeindexed. The arrows mark the one-to-one correlation between thesingle-wire leaky mode resonances and the photocurrent enhancementpeaks.

The figure also shows the predicted absorption spectra (dotted line) forcylindrical NWs based on the well-established Lorentz-Mie lightscattering formalism. In order to compare the experimental andtheoretical results, both datasets are given in terms of the spectralabsorption efficiency, Qabs, which is defined as the absorptioncross-section normalized to the geometrical cross-section of the NW.Distinct peaks can be observed in the Qabs spectra that exhibit asubstantial dependence on the NW size, consistent with the excitation ofLMRs. The good agreement between the experimental and calculated spectrasuggests that the LMR-enhanced absorption in the NWs can be approximatedby the Lorentz-Mie formalism and by assuming a homogeneous host mediumof unity refractive index. The good agreement is not unexpected as therelevant modes are well-confined to the high-index NW and theinteraction with the substrate is minimal. Although even betteragreement can be obtained using more time-consuming full-fieldsimulations that include the presence of a substrate, the analyticLorentz-Mie theory allows for a rapid first-order optimization of theNW-based PV cells as discussed below.

In order to optimize PV performance with LMRs, we first aim to identifythe optimum SiNW diameter, d, that will maximize the absorption ofsunlight and thus short circuit current density, JSC(d). To this end, wecalculate Qabs (λ,d) for SiNWs of different diameters and integrate thecalculated absorption with the spectral photon flux density delivered bythe sun, Fs(λ) . This integral gives the short-circuit photocurrentdensity of a single NW solar cell, JSC(d)=q ∫ Fs(λ)Qabs (λ,d) dλ. Here,q is the charge carried by one electron. In the calculation we assumedan internal quantum efficiency of 100%, which has recently beendemonstrated with NW junction devices. The current density refers to thephotocurrent divided by the geometrical cross-sectional area of the NW(d·l, where l is the length of the NW). In order to make a comparison toplanar Si structures, we have also calculated the absorption of light ina surface layer of a crystalline Si wafer with the same thickness as thewire. For these calculations, we have used the well-established opticalproperties of single-crystalline silicon. As shown in the upper panel ofFIG. 4 b, the NW produces a much larger photocurrent density than thatof bulk Si for the same volume of material. For example, an80-nm-diameter NW experiences a 300% enhancement in the photocurrent perunit volume.

The role of the LMRs in the enhancement can clearly be seen in atwo-dimensional plot of the absorption efficiency Qabs versus A and d(FIG. 4 b lower panel). This figure shows the absorption enhancementsrelated to the various transverse electric (TEml) and transversemagnetic (TMml) LMRs of a NW illuminated under normal incidence, where mand l are the azimuthal mode number and radial order of the resonancesrespectively. A comparison between the upper and lower panels of FIG. 4b reveals a one-to-one correspondence between the peaks in thephotocurrent enhancement and the spectral locations of the LMRs. Asillustrated by the arrows in FIG. 4 b, the first enhancement peak (theenhancement peaks are counted as first, second, third, etc. in the orderof ascending diameter) finds its origin in the excitation of the lowestorder LMR, which is TM 01 . This peak is seen in NWs that are very small(˜10 nm) compared to the wavelengths from the incident sun light; itarises from an electrostatic dipole excitation of the wire. The secondand the third photocurrent peaks can be correlated to the followinghigher order LMRs, TM 11 /TE 01 and TM 21 /TE 11 , respectively. Fromthis analysis, the role of the various LMRs in enhancing thephotocurrent and thus the PV performance is evident.

The LMRs not only enhance the NW's ability to absorb sunlight, they alsocan substantially minimize the dependence of the light absorption onillumination angle. Due to the cylindrical symmetry, a change in theillumination angle in the plane normal to the wire does not affect thelight absorption. FIG. 5 a shows dependence of the normalized JSC on theillumination angle for various diameter (20 nm, 80 nm, 140 nm, and 300nm) silicon nanowires. The angle-dependence of the photocurrent inplanar bulk silicon is also given for comparison. FIG. 5 b showsmeasured (upper) and calculated (lower) absorption spectra of100-nm-diameter silicon nanowires illuminated at different incidenceangles (20°, 30°, 50°, and 90°). We can see that the photocurrent in theNW generally shows less dependence on the incident angle than that of aplanar structure except for very small (˜20 nm) wires. For the comingdiscussion, it is worth noting that NWs with diameters of ˜80-100 nmexhibit a particularly small dependence of JSC on incident angle; theirphotocurrent is more-or-less constant until the incident angle is lessthan 20°.

The angle-dependence of the NW photocurrent can be understood from theangle-dependence in the excitation of LMRs. This angle-dependence hasrelatively simple geometric contributions and more complex materialscontributions, which result from dispersion. In order to selectivelyexplore the effects of geometry, the absorption efficiency Qabs wascalculated as a function of a dimensionless size parameter nkd/2 (k,wavevector of the incident light in free space) and the illuminationangle for a frequency-independent refractive index, n=4+0.03 i. Thisindex value is representative of a high-index, absorbing semiconductorNW. Among all the LMRs for this example, it was found that the secondorder LMRs (i.e., TE 11 and TM 21 ) exhibit the weakest angle dependenceand that the angle dependence is quite small for higher LMRs as well.Based on these results, it is natural to expect a substantial absorptionenhancement and a weak angle-dependence in the response of SiNW solarcells when the second order LMRs provide a large contribution to theabsorption of sunlight. FIG. 4 b shows that c-SiNW sizes in the rangefrom 80-100 nm provide a good wavelength match between the second orderLMRs resonance and the peak of the solar spectrum (near 500 nm). Moregenerally, the peak of the solar spectrum can be regarded as falling ina range from about 475 nm to about 525 nm, and it is preferred for thesingle-wire LMRs to have an absorption peak in this range for solar cellapplications. The anticipated weak angle-dependence of the absorption insuch SiNWs is confirmed by experimental and calculated absorptionspectra on a 100-nm-diameter c-SiNW, as shown in FIG. 5 b.

LMRs are essentially morphology-dependent resonances, arising from thefinite NW size and the large refractive index contrast of the NW withrespect to its surroundings. It should thus be expected that anyhigh-index semiconductor used in solar applications could benefit fromthese types of resonances. FIG. 6 a (upper) is a plot of short circuitphotocurrent density JSC in nanowires of several major photovoltaicmaterials, including CuInGaSe, Ge, CdTe, amorphous Si, and GaAs, and(lower) is a plot of photocurrent enhancement in the nanowires comparedto their bulk counterparts. FIG. 6 b is a plot of minimized dependenceof JSC of various semiconductor nanowires on the incident angle. Thediameters of the nanowires are CuInGaSe, 180 nm, Ge, 140 nm, α-Si, 120nm, CdTe, 140 nm, and GaAs, 120 nm, respectively. Those diameters matchthe excitation of the second order LMRs. All materials systems that havebeen modeled or measured show significant enhancements and similartrends in the dependence on the nanowire size. Preferably, the diameterof the nano-wires is in a range from 120 nm to 200 nm. For all of thesemiconductors, JSC tends to show good enhancements and littleangle-dependence when the NW size is optimized to again match the secondpeak in the plots of photocurrent vs. size (FIG. 6 b). For example, a130-nm-diameter α-Si NW may generate JSC of ˜24 mA/cm² out of ˜49 mA/cm²that is available from the AM 1.5 spectrum. For NWs larger than 100 nm,JSC is approximately independent of size; these larger wires experienceonly minor gains in absorption at long wavelengths where the solarirradiance is relatively small.

Optical antenna resonances are not limited to a perfect cylindricalgeometry and are a general feature of high-index nanostructures. FIG. 7a is a plot of calculated short-circuit photocurrent density JSC for1-dimensional amorphous Si structures of circular, rectangular,hexagonal and triangular cross-section as a function of size. The insetschematic illustrates the way to compare the size for differentstructures with a double-headed arrow, and the thick solid arrowindicates the illumination geometry used in the calculations. Nano-wireshaving any cross section shape can be used to practice the invention.Suitable cross section shapes include, but are not limited to: circles,squares, rectangles, ellipses, triangles, and hexagons. FIG. 7 b is aplot of calculated absorption spectra of these 1-dimensional structuresin a size lying in the regime that corresponds to their secondenhancement peaks shown in a. Specifically, the size is 180 nm fortriangular cylinder and 130 nm for all other structures. The results fora cylinder are also given for reference. The spectra are qualitativelyvery similar. They all feature large absorption efficiencies (close tounity) over a wide frequency range. The observed differences in Qabs areprimarily due to the different volumes of material in the structures.These results indicate that similar types of optical antenna resonancesare excited in all the structures.

The above-described principles can guide the rational design ofhigh-efficiency NW-based PV cells. This is illustrated with a PV celldesign employing an array of α-Si NWs on a glass substrate, as shown inthe inset of FIG. 8 a. From the discussion on FIGS. 6 a-b, we learntthat a 130 nm α-Si NW shows both a high short circuit current and abroad angular response. We take this NW as a building block for aNW-array cell. If its antenna properties can be preserved in the arrayconfiguration, the cell should generate a substantially higher JSC thanan unstructured film of the same thickness, despite the lower volume ofsemiconductor. In order to keep the discussion as general as possible,we calculate the cell performance without making assumption about theelectrical design for the charge collection (e.g. pn-junction) nor do wemake detailed assumptions about the electrical materials quality; weagain simply assume a 100% internal quantum efficiency for the NWs andhave the enhancements in JSC directly reflect enhancements in theabsorption of sunlight. This computation therefore provides an intrinsicmeasure of the efficiency gain in the use of NWs as compared to thinfilms. To visualize the transition from a continuous film to an array ofwell-separated NWs, we calculated the JSC for a top-illuminated array of130 nm rectangular NWs as a function of their spacing and compared it tothe JSC of a 130 nm thick film, which is 11.3 mA/cm² (FIG. 8 a). Morespecifically, FIG. 8 a shows calculated photocurrent density JSC of anarray of 130-nm-wide square nanowires as a function of the nanowireseparation. The left-side vertical axis indicates the photocurrentnormalized to that of a continuous film (zero separation). The optimumNW cell with a spacing of 130 nm features a ˜25% increase in JSC, whileusing only 50% of the material (250% increase in current per unit volumematerial). Preferably, the spacing of the nano-wires in the array is ina range from 120 nm to 200 nm.

Our data indicates that the optical resonances seen in the individualNWs play an important role in enhancing the absorption of sunlight bythe array. Their importance is first of all reflected in the weakerdependence of JSC on the illumination angle for the NW array as comparedto a film (unpatterned) materials This behavior is seen on FIG. 8 b,which shows calculated dependence of the photocurrent density JSC on theillumination angle for the array with various spacing (50 nm, 130 nm and260 nm) and a 130 nm thick film. The incident angle is changed in theplane where the wire axis lies in, as shown. This figure shows that forincreasing NW spacings the angular response broadens, retrieving thevery broad angular response of individual NWs for sufficiently largespacings. The broadband nature of the absorption spectra as well as thelarge magnitude of Qabs and the electric field distribution inside eachNW in an optimized (130 nm spacing) array also reflect/resemble those ofindividual NWs. This behavior is seen on FIG. 8 c, which showscalculated absorption spectra of a 130-nm-wide square nanowire in thearray with different separations of 30 nm, and 130 nm. The dash-dottedline is the absorption spectra of a single nanowire on the samesubstrate. The broad absorption spectrum of the array with the 130 nmspacing strongly resembles that of a single nanowire.

From the above discussion, it is apparent that the intrinsic and strongoptical antenna effects in semiconductor NWs offer a very general andhighly effective PM strategy for solar cells. This approach may form thebasis for a valuable new PV platform technology that is applicable toall semiconductor materials and a wide variety of one-dimensionalnanostructures. In addition to the straight, periodic NW arraysdiscussed here, complex interconnected semiconductor patterns oraperiodic arrays are expected to exhibit similar resonances, opening upa large parameter space for study and optimization. To further boost theperformance of these devices, one may also add more conventional PMtechniques such as AR-coatings and backreflectors. The requiredstructures are quite large (>100 nm) and can be fabricated usingstandard, scalable thin film deposition and patterning technologies.Straight NW antennas can also be mass-produced and deposited usinglow-cost procedures such as roll-to-roll ink jet printing on inexpensiveplastic substrates. In addition to the possibilities for solar energyapplications, this approach is quite general and could also be appliedto ultra-fast photodetectors, imagers, sensors, and in reverse for solidstate-lighting.

The preceding description has been by way of example as opposed tolimitation, and many variations of the given examples also constitutepractice of the invention. For example, the nano-wire arrays can beperiodic, as in the preceding examples, or aperiodic. FIG. 9 a shows aperiodic nano-wire array 904 on a substrate 902. FIG. 9 b shows anaperiodic nano-wire array 906 on substrate 902.

The examples given above relate to single-wire leaky mode resonances.However, the present principles are also applicable to other cases wherean array resonance arises from a leaky mode resonance of one or morenano-wires (e.g., from pairs of coupled nano-wires).

The preceding description has mainly concentrated on the solar cellapplication. However, the present approach for providing increasedefficiency of optical absorption is broadly applicable. Applicationsinclude, but are not limited to: solar energy, photodetection,photocatalysis, and imaging. In each case, incident radiation having aspectral intensity peak can be more efficiently detected/collected byspectrally aligning the incident spectral intensity peak with an arrayresonance of optical absorption of a nano-wire array.

1. Apparatus for absorbing solar radiation, the apparatus comprising: asubstrate; and an array of two or more semiconductor nano-wires disposedlaterally on the substrate; wherein the array has one or more arrayresonances of optical absorption; wherein each of the array resonancesarises from a corresponding leaky mode resonance of one or more of thenano-wires; wherein each of the leaky mode resonances has acorresponding spectral absorption peak; wherein one or more dimensionsof the nano-wires are selected such that a selected one of the spectralabsorption peaks is substantially at 500 nm.
 2. The apparatus of claim1, wherein the selected spectral absorption peak is in a range between475 nm and 525 nm.
 3. The apparatus of claim 1, wherein the selectedspectral absorption peak corresponds to a leaky mode resonance that is aTE 01 or a TM 11 resonance.
 4. The apparatus of claim 1, wherein across-section shape of the nano-wires is selected from the groupconsisting of circle, square, rectangle, ellipse, triangle, and hexagon.5. The apparatus of claim 1, wherein a diameter of the nano-wires is ina range from 10 nm to 3000 nm.
 6. The apparatus of claim 1, wherein thesemiconductor nano-wires include a single-crystalline, polycrystalline,or amorphous material selected from the group consisting of: Si, CdTe,GaAs, CuInGeSe, copper-zinc-tin-sulfur (CZTS) compositions, and Ge. 7.The apparatus of claim 1, wherein a spacing of the nano-wires in thearray is in a range from 10 nm to 500 nm.
 8. The apparatus of claim 1,further comprising two terminals connected to the apparatus such thatelectrical power can be extracted from the terminals when the apparatusis illuminated.
 9. The apparatus of claim 8, wherein current carriersgenerated in the nano-wires by optical absorption travel toward theelectrodes in a vertical direction, relative to the substrate.
 10. Theapparatus of claim 1, further comprising an array of concentrator lensesdisposed to focus incident radiation onto the nano-wires.
 11. Theapparatus of claim 1, wherein the array of two or more semiconductornano-wires is an aperiodic array.
 12. The apparatus of claim 1, whereinthe array of two or more semiconductor nano-wires is a substantiallyperiodic array.
 13. A method for absorbing electromagnetic radiationhaving an incident radiation spectrum with a spectral intensity peak,the method comprising: providing an array of two or more semiconductornano-wires disposed laterally on a substrate; wherein the array has oneor more array resonances of optical absorption; wherein each of thearray resonances arises from a corresponding leaky mode resonance of oneor more of the nano-wires; wherein each of the leaky mode resonances hasa corresponding spectral absorption peak; wherein one or more dimensionsof the nano-wires are selected such that one of the spectral absorptionpeaks is substantially spectrally aligned with the spectral intensitypeak.
 14. A method for solar energy collection comprising the method ofclaim
 13. 15. A method for photodetection comprising the method of claim13.
 16. A method for photocatalysis comprising the method of claim 13.17. A method for imaging comprising the method of claim 13.